def eratosthenes_sieve(n):
    # Create a candidate list within which non-primes will be
    # marked as None; only candidates below sqrt(n) need be checked.
    candidates = list(range(n+1))
    fin = int(n**0.5)

    # Loop over the candidates, marking out each multiple.
    for i in range(2, fin+1):
        if candidates[i]:
            # from 2i in steps of i, set each to None.
            candidates[2*i::i] = [None] * len(candidates[2*i::i])

    # Filter out non-primes and return the list.
    return [i for i in candidates[2:] if i]